Editing Imaginary unit (section)

===Root of {{math|''x''<sup>2</sup> + 1}}===
[[Polynomial]]s (weighted sums of the powers of a variable) are a basic tool in algebra. Polynomials whose [[coefficient]]s are real numbers form a [[ring (mathematics)|ring]], denoted <math>\R[x],</math> an algebraic structure with addition and multiplication and sharing many properties with the ring of [[integer]]s.

The polynomial <math>x^2 + 1</math> has no real-number [[root of a polynomial|roots]], but the set of all real-coefficient polynomials divisible by <math>x^2 + 1</math> forms an [[ideal (ring theory)|ideal]], and so there is a [[Polynomial ring#Quotient ring|quotient ring]] <math>\reals[x] / \langle x^2 + 1\rangle.</math> This quotient ring is [[isomorphism|isomorphic]] to the complex numbers, and the variable <math>x</math> expresses the imaginary unit.